Artinian and noetherian hypercentral groups

Noetherian and Artinian Lattices

Copyright q 2012 Derya Keskin T ¨ utüncü et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. It is proved that if L is a complete modular lattice which is compactly generated, then RadL/0 is Artinian if, and only if for every s...

Artinian and Noetherian Rings

Noetherian and Artinian ordered groupoids - semigroups

Chain conditions, finiteness conditions, growth conditions, and other forms of finiteness, Noetherian rings and Artinian rings have been systematically studied for commutative rings and algebras since 1959. In pursuit of the deeper results of ideal theory in ordered groupoids (semigroups), it is necessary to study special classes of ordered groupoids (semigroups). Noetherian ordered groupoids (...

Subrings of Artinian and Noetherian Rings

An easy consequence of this is that a left Noetherian (respectively left Artinian) ring which is finitely generated over its center is right Noetherian (respectively right Artinian). Theorem 1 follows easily from Theorem 2, which gives a partial converse to the following standard fact: IfR C S are rings, and ifQ is an injective R-module, then Hom~(S, Q) is an injective S-module (this follows, f...

Positive Implicative-Artinian and Positive Implicative Noetherian Hyper Bck-Algebras

The notion of intuitionistic fuzzy positive implicative hyper BCK-ideals of type-1, 2... 8 of hyper BCK-algebras was introduced in 2012 by Durga Prasad, Satyanarayana and Ramesh. In this paper, we investigate some related properties of intuitionistic fuzzy positive implicative hyper BCK-ideals of types-1. We characterize positive implicative Artinian (shortly, PI-Artinian) hyper BCK-algebras of...